/*********************************************************************
Copyright (C) :    University of Michigan
Project:           ENG101/200 - Class example
File:              randomIntegrate.cpp
Purpose:           Integrates a function by random sampling
Compiler:          g++
Programmer:        Alex Bielajew
Start Date:        09/28/10
*********************************************************************/

//File: randomIntegrate.cpp
#include <iostream>
#include <iomanip>
#include <cstdlib> // Need for rand() and srand()
#include <cmath> // Need for exp(), the exponential function
                 // and abs(), the absolute value function
                 
using namespace std;

/* Define a conversion function that converts the int returned from
   rand() to a double between 0.0 and 1.0 inclusive
*/
#define MYRAND (static_cast<double>(rand())/RAND_MAX)

int main(void)
{  int nDarts = 100000000, under = 0;
   double Ans = 1 - exp(-1);
   for(int i = 1; i <= nDarts; i = i + 1)
   {  double xDart = MYRAND; 
      double yDart = MYRAND;
      if (yDart <= exp(-xDart)) under = under + 1;
      if (0 == i%1000000) // Every million times
      {  double ans = static_cast<double>(under)/i;
         cout << setiosflags(ios::fixed) << setprecision(8) 
	      << "#" << setw(10) << i 
	      << ": I = " << setw(10) << ans
	      << ", Delta = " << abs(1 - exp(-1) - ans) << "\n";
      }
   }
   return 0;
}